Darren Fletcher scored his first goal to help third-placed Manchester United stay in touch with Chelsea and Arsenal.
Fletcher slid the ball in after nine minutes when Mark Schwarzer was only able to parry a cross from Ryan Giggs.
Before the goal, Cristiano Ronaldo had drawn an instinctive save from the Boro keeper as well as hitting the woodwork.
Late on Giggs wrapped up the points when he pounced on Eric Djemba-Djemba's pass, got in front of Gareth Southgate, before poking the ball past Schwarzer.
In a first-half dominated by United, Boro were never quite able to get to grips with the visitors' array of attacking talent, notably the way Ronaldo and Giggs continually swapped wings.
In Fletcher, United also had the game's outstanding midfield player, though Boudewijn Zenden and Stewart Downing work tirelessly to redress the balance in that area for Boro.
In an effort to pep up the Boro attack, manager Steve McClaren replaced Joseph-Desire job with Szilard Nemeth at the interval.
The change brought about a more adventurous approach from Boro, but with Rio Ferdinand superbly marshalling the United defence, McClaren's side were never able to produce any clear chances.
Ferdinand's superb defensive display was typified 15 minutes from the end when he cut out a cross from Downing as Nemeth lurked just behind him.
Giggs capped another fine performance for United when good close control allowed him to get ahead of Southgate and then dink the ball past Schwarzer.
That Boro would prove incapable of forcing United goalkeeper Roy Carrol to make a single save had seemed an unlikely outcome when in the second minute Downing swung in a dangerous cross that almost found Jimmy Floyd Hasselbaink.
Having survived that early scare, United proceeded to lay seige to the Boro goal.
Schwarzer had to make a reaction save to deny Ronaldo after a free-kick from Giggs was deflected into the Portuguese international's path by Roy Keane.
Soon afterwards Ronaldo hammered the ball against the woodwork following another deflection, this time from a Scholes shot, though the United winger had looked suspiciously offside when he gathered the ball.
Having applied a tourniquet to the Boro defence, United tightened it courtesy of Fletcher's goal.
Giggs broke away down the left and although Schwarzer got his hands to the cross he was unable to hold it and Fletcher gleefully side-footed home.
Amid all this United pressure, Boro's best effort after Fletcher's goal was a Zenden shot that went over the bar.